Graph filtering,which is founded on the theory of graph signal processing,is proved as a useful tool for image denoising.Most graph filtering methods focus on learning an ideal lowpass filter to remove noise,where cle...Graph filtering,which is founded on the theory of graph signal processing,is proved as a useful tool for image denoising.Most graph filtering methods focus on learning an ideal lowpass filter to remove noise,where clean images are restored from noisy ones by retaining the image components in low graph frequency bands.However,this lowpass filter has limited ability to separate the low-frequency noise from clean images such that it makes the denoising procedure less effective.To address this issue,we propose an adaptive weighted graph filtering(AWGF)method to replace the design of traditional ideal lowpass filter.In detail,we reassess the existing low-rank denoising method with adaptive regularizer learning(ARLLR)from the view of graph filtering.A shrinkage approach subsequently is presented on the graph frequency domain,where the components of noisy image are adaptively decreased in each band by calculating their component significances.As a result,it makes the proposed graph filtering more explainable and suitable for denoising.Meanwhile,we demonstrate a graph filter under the constraint of subspace representation is employed in the ARLLR method.Therefore,ARLLR can be treated as a special form of graph filtering.It not only enriches the theory of graph filtering,but also builds a bridge from the low-rank methods to the graph filtering methods.In the experiments,we perform the AWGF method with a graph filter generated by the classical graph Laplacian matrix.The results show our method can achieve a comparable denoising performance with several state-of-the-art denoising methods.展开更多
Graph filtering is an important part of graph signal processing and a useful tool for image denoising.Existing graph filtering methods,such as adaptive weighted graph filtering(AWGF),focus on coefficient shrinkage str...Graph filtering is an important part of graph signal processing and a useful tool for image denoising.Existing graph filtering methods,such as adaptive weighted graph filtering(AWGF),focus on coefficient shrinkage strategies in a graph-frequency domain.However,they seldom consider the image attributes in their graph-filtering procedure.Consequently,the denoising performance of graph filtering is barely comparable with that of other state-of-the-art denoising methods.To fully exploit the image attributes,we propose a guided intra-patch smoothing AWGF(AWGF-GPS)method for single-image denoising.Unlike AWGF,which employs graph topology on patches,AWGF-GPS learns the topology of superpixels by introducing the pixel smoothing attribute of a patch.This operation forces the restored pixels to smoothly evolve in local areas,where both intra-and inter-patch relationships of the image are utilized during patch restoration.Meanwhile,a guided-patch regularizer is incorporated into AWGF-GPS.The guided patch is obtained in advance using a maximum-a-posteriori probability estimator.Because the guided patch is considered as a sketch of a denoised patch,AWGF-GPS can effectively supervise patch restoration during graph filtering to increase the reliability of the denoised patch.Experiments demonstrate that the AWGF-GPS method suitably rebuilds denoising images.It outperforms most state-of-the-art single-image denoising methods and is competitive with certain deep-learning methods.In particular,it has the advantage of managing images with significant noise.展开更多
基金This work is supported by National Natural Science Foundation of China[61673108,41706103]The initials of authors who received these grants are LZ and YZ,respectively.It is also supported by Natural Science Foundation of Jiangsu Province,China[BK20170306]The initials of author who received this grant are YZ.
文摘Graph filtering,which is founded on the theory of graph signal processing,is proved as a useful tool for image denoising.Most graph filtering methods focus on learning an ideal lowpass filter to remove noise,where clean images are restored from noisy ones by retaining the image components in low graph frequency bands.However,this lowpass filter has limited ability to separate the low-frequency noise from clean images such that it makes the denoising procedure less effective.To address this issue,we propose an adaptive weighted graph filtering(AWGF)method to replace the design of traditional ideal lowpass filter.In detail,we reassess the existing low-rank denoising method with adaptive regularizer learning(ARLLR)from the view of graph filtering.A shrinkage approach subsequently is presented on the graph frequency domain,where the components of noisy image are adaptively decreased in each band by calculating their component significances.As a result,it makes the proposed graph filtering more explainable and suitable for denoising.Meanwhile,we demonstrate a graph filter under the constraint of subspace representation is employed in the ARLLR method.Therefore,ARLLR can be treated as a special form of graph filtering.It not only enriches the theory of graph filtering,but also builds a bridge from the low-rank methods to the graph filtering methods.In the experiments,we perform the AWGF method with a graph filter generated by the classical graph Laplacian matrix.The results show our method can achieve a comparable denoising performance with several state-of-the-art denoising methods.
基金This work is supported by Natural Science Foundation of Jiangsu Province,China[BK20170306]National Key R&D Program,China[2017YFC0306100].The initials of authors who received these grants are YZ and JL,respectively.It is also supported by Fundamental Research Funds for Central Universities,China[B200202217]Changzhou Science and Technology Program,China[CJ20200065].The initials of author who received these grants are YT.
文摘Graph filtering is an important part of graph signal processing and a useful tool for image denoising.Existing graph filtering methods,such as adaptive weighted graph filtering(AWGF),focus on coefficient shrinkage strategies in a graph-frequency domain.However,they seldom consider the image attributes in their graph-filtering procedure.Consequently,the denoising performance of graph filtering is barely comparable with that of other state-of-the-art denoising methods.To fully exploit the image attributes,we propose a guided intra-patch smoothing AWGF(AWGF-GPS)method for single-image denoising.Unlike AWGF,which employs graph topology on patches,AWGF-GPS learns the topology of superpixels by introducing the pixel smoothing attribute of a patch.This operation forces the restored pixels to smoothly evolve in local areas,where both intra-and inter-patch relationships of the image are utilized during patch restoration.Meanwhile,a guided-patch regularizer is incorporated into AWGF-GPS.The guided patch is obtained in advance using a maximum-a-posteriori probability estimator.Because the guided patch is considered as a sketch of a denoised patch,AWGF-GPS can effectively supervise patch restoration during graph filtering to increase the reliability of the denoised patch.Experiments demonstrate that the AWGF-GPS method suitably rebuilds denoising images.It outperforms most state-of-the-art single-image denoising methods and is competitive with certain deep-learning methods.In particular,it has the advantage of managing images with significant noise.
文摘由于电网企业不断加快数字化转型,利用北斗定位技术将自动获取区域内光伏计量装置经纬度这一关键技术参数。文章充分利用分布式光伏集群内光伏发电装机位置空间相关性,提出一种在弱监督下基于图滤波与支持向量数据描述(support vector data description,SVDD)的分布式光伏集群发电异常检测方法。首先建立分布式光伏集群发电图数据结构模型,通过加权邻接矩阵描述分布式光伏发电点空间耦合性,其次构造图高通滤波器将时域参数转化为频域参数,然后通过SVDD算法优化图滤波结果,进一步挖掘图高通滤波器阈值与输出功率数据之间的关系。结果表明,采用图滤波器和SVDD算法模型方法在分布式光伏发电异常检测精度上有显著提高。
